Job Training Program: Difference-in-Differences

Job Training Program Evaluation

• A city offers a job training program to residents aged 40+ who have been unemployed for at least 20 weeks.
• The goal is to estimate the program's effect on future employability using a difference-in-differences strategy.
• Employment data is available only from this city, with varying ages and unemployment experiences.
• It's known that training was widespread among eligible residents, but individual training receipt isn't observed.

Treatment and Control Groups

• Treatment Group: Residents 40+ unemployed for 20+ weeks, widespread program knowledge exists but individual training receipt is unverified.
• Control Group: Residents unemployed for fewer than 20 weeks.
  • Below 40 years old, unemployed for at least 20 weeks.
  • Below 40 years old, unemployed for less than 20 weeks.
  • Above 40 years old, unemployed for less than 20 weeks.

Conceptual Framework Equations

• h represents work hours, with the training policy aiming to increase it.
• T denotes treatment, and C denotes control
• hiTpre = alphaT + B1(age) + B2(weeks unemployment) + error (T, i, pre)
• hiTpost = alphaT + Growth + B1(age) +B2(weeks unemployment) + error (T, i, post)
• hiCpre = alphaC + B1(age) + B2(weeks unemployment) + error hi (C, i, pre)
• hiCpost = alphaC + B1(age) + Growth + B2(weeks unemployment) + error (C, i, pre)

h hi, PRE = α + γτ + Ei

• hi, POST = a + γτ + δ + τ + €¡

hi, PRE = a + c + €¡ C

• hi POST = a + c + d + €¡

Addressing Pre-Existing Differences

• The difference-in-differences method eliminates pre-existing differences between groups
• DID compares two groups with pre-existing differences atop the treatment, assuming that the effect of the difference is constant over time.
• In DID, the time-invariant effect is subtracted out in the first difference, preventing it from contaminating the comparison in the second difference
• Treatment and comparison groups may have different levels of the outcome, but pre-treatment trends should be the same.
• Without treatment, it is expected that the outcomes for the treatment and comparison groups would change at the same rate

DID (Difference in Differences) Strategies

• Formulate 4 regression equations using hours of work as the dependent variable; the "post" variable will include a "Growth" variable
• Subtract pre from post for both groups, then subtract the amount from control from amount for treatment to see difference
• A positive number demonstrates program efficacy, with hours of work higher in treated groups after the program
• Assume other things equal so errors = 0, differences-in-differences
• Data needed:
  • Unemployment rates before and after the training program in the city
  • Unemployment rates before and after in a similar city without the program
  • Economic growth in both cities during the time period
• Create a dummy variable indicating if job training occurred (1) or not (0) & use synthetic control to show city similarity
• Use 4 equations: Regress the unemployment rate on a dummy variable indicating if job training occurred
  • Two equations for the city being tested: the first regresses on the job training variable, and the second adds a "growth" variable
  • Two equations for the control city: the first regresses on the dummy variable, and the second adds a "growth" variable
• Subtract first two, the second two, and subtract the results of each to create "differences in differences", measure whether or not relationship between program and unemployment rate is negative
• Growth variable accounts for other affecting factors, other factors aside from growth are taken into account by using similar city
  • Another regression for people in the same city in different areas, may use borders like Holmes (1998) can account for other factors such as the city having different growth. Accounting for lag? Measure rates for same individuals 2 years later

Reasons to Study Labor Supply Behavior

• A major part of most people's lives, and can help people learn how to get jobs e.g. during unemployment or when trying to know how to create more jobs as a governor
• Government revenue comes largely from income taxes: how to finance publicly provided goods, national defense, education, etc.
  • Optimal taxation based on labor supply behavior will maximize these
• Macroeconomics models based on people renting labor: better macroeconomic models with labor supply involved as a variable helps us to explain economic downturns better, and how to explain macroeconomic disasters, or assess impact of monetary policy

Average Weekly Hours of Work Decline

• Average weekly hours of work declined throughout the 20th century because of a static labor supply wage increasing
• The graph depicts the net effect that a wage change has on the labor supply behavior in neoclassical frame (A to C)
• Average weekly hours of work in the 20th century likely declined because of a rise in wages (making the budget constraint slope steeper)
• Substitution effect (A to B): leisure is more expensive and the greater wage means we can consume more so people substitute towards more hours (more work)
• Income effect (B to C): people work less because they are wealthier overall and can "afford" more leisure (more leisure)
• Income effect outweighs the substitution effect, the net change is that people's work hours have declined

Backward-Bending Labor Supply Curve

• A backward-bending supply curve shows curve in which, in a certain period of time, an individual will supply more labor initially as their wages increase.(substitution effect dominates income effect)
• However, they will reach a point where they are wealthy enough that they feel comfortable supplying less work hours in order to enjoy more leisure time (income effect dominates substitution effect)
• The time where workers supply more hours of labor is where the substitution effect is greater than income effect, while the time where workers supply less hours is where the income effect is greater than the substitution effect
• A market labor supply is not backward-bending because it represents the labor supply behavior for ALL individuals in the market, while the backward bending curve represents the supply of work HOURS for an INDIVIDUAL worker
• Most workers do not reach an income level where they will end up supplying less hours and, if wages rise, the new people entering the market will offset anyone who would decrease hours.
• People supply labor at different prices, earn different wages

Transitory Wage Changes and Labor Supply

• Neoclassical (Farber): Cov (wage, hours) > 0

  • Work until marginal benefit (wage) is just equal to marginal cost ("shadow value of time")
  • Positive elasticity between the two meaning that taxi drivers will work more hours with a transitory wage increase
  • More wage, moe work
  • Intertemporal substitution (the process of maximizing utility by allocating resources across time)

• Behavioral: Cov(wage, hours) < 0

  • Loss aversion & reference dependence: workers make daily income expectation -- reference point
  • If wage is close to expectation, supply labor to meet income target
  • Anticipated wage increase: increase the reference point, supply more hours, positive elasticity
  • Unanticipated wage increase (transitory): reference point is the same, supply less hours, negative elasticity
  • Individuals are loss averse, there is a kink in the utility function at the reference income level, with higher marginal utility below the kink and lower marginal utility above the kink

• Taxi drivers are a good population because they have lots of control over their hours

• Overall pattern of data: drivers tend to respond positively to unanticipated as well as anticipated increases in earnings opportunities

  • positive elasticities, newer drivers w/ smaller elasticities more likely to exit industries while those who remain become better optimizers Data limitation: tipping ignored (no info on cash taps)

• 3 lessons from paper:

• 1. The neoclassical model is a better explanation for behavior of taxi drivers, and may be a good representation for labor supply in general
  • 2. Systematic measurement error is a big problem and can cause erroneous conclusions
  • (Farber uses instrumental variables to take away division bias; division bias = measurement error in hours of work)
  • 3. Allowing individuals to dictate their own labor supply elasticity induces a range of elasticity, but with the large majority being positive

Elasticity of Labor Supply and Division Bias

• Previous division bias: wage/hours (too low/high) : denominator systematically underestimated & numerator systematically overestimated due to measurement error.
  • Ex. misreporting, transcription, tips ignored, breaks taken in between shifts that are not recorded
  • whole thing upward biased
  • The OLS estimate may be downward biased due to "division" bias if there is specification or measurement error - negative bias in the estimated wage elasticity Even if the true elasticity is positive or zero, division bias can cause the estimated elasticity to be negative. Reasons to suspect division bias:
• 1. Data imperfectly transcribed from potentially erroneous hand recordings
  • 2. Trip sheets do not record tip income, which likely varies
  • 3. May be breaks taken in the middle of shifts
• hi = alpha + Betawi, wi = Ii/hi, hi and wi are mechanically corrected, will always create a systematic measurement error where wages will move inversely with hours
• Farber's method : instrumental variable (IV) estimation: used the hours of other workers which had no correlation with individual worker's wages to infer the effect on hi
  • No measurement error
  • Found that hours were actually much higher than previous studies that proved Behavioral theory

Effects of a Proportional Wage Tax

• Tax revenue depends on behavior responses
• Income effect > substitution effect
• Work more, less leisure:
• Individual increases hours in order to have more money to consume (to keep same income)
• Proportional tax decrease income than before tax
• Graph shows an effective decrease in wages, and a pivot downward from A -> C, increase in work hours, decrease in leisure, point where indifference curve is tangent to the budget constraint moves left
• Decrease hr Budget Constraint e indifference Curvese Labor Supply

Income effects > substitution effect Less work, more leisure Individuals decrease work hours since leisure becomes cheaper and they can just substitute away The tax increase induces workers to work less through both substitution and income effects. The substitution effect arises from the higher opportunity cost of leisure relative to work, leading to a decrease in labor supply. The income effect, resulting from the decrease in after-tax income, may reinforce the substitution effect, further reducing labor supply.

Social Security Payroll Tax

• The Social Security payroll tax applies only to earnings up to a cap ($176,100 in 2025).
• Social Security Payroll tax - 6.2% on income below cap (cap = $176100 in 2025): low-middle level income work hour, if SE matters a lot & wage +: Work hour 4 if If matters a lot
• Redistribution of income, high income ppl pay their share High income ppl not as sensitive to wage changes, tax rates & potentially more government revenues since there is more taxation at the top Low income ppl are no longer disproportionately penalized Wide distribution and thick right tail, means tax acts as low-efficiency cost lump sum Disincentive to earn, penalizing people for contributing more to society & Could potentially reduce government revenue bc high income ppl reduce earnings: Less productivity since highest earners work less Behavioral parameter : Whether or not government revenue increases from this policy depends on whether the income or substitution effect is stronger Elasticity of reported income with respect to the wage Substitution effect induces high income ppl to earn to enjoy more leisure Income effect induces them to work more to consume more in the future Diamond and Saez (2011) argue to increase taxes on high earners, Mankiw et. al (2009) argue to decrease

Alternative Income Support Programs

• Government benefit B to people not working: Income Support Programs -- Incone support for non-working adults ($B), Encourgare this person to enjoy a higher level of consumption & utility when not working & Disincentive to work not eligible for any financial support Hours of work decreases, consumption increases
• Guaranteed income floor F: Below the floor, people who are working supply the same amount of hours but consume more due to the income floor, makes sure ppl can earn a living even if they aren't working or are working very little
• ppl both in & out of labor force can be eligible & there will exist workers who opt not to work be utility is maximized by not working at all & just receiving the income floor amount & There is a disincentive to work since up to a certain point you earn the same amount no matter how many hours you work, an incentive to substitute in more leisure w/o sacrificing wage & cost to the government
• Earned Income Tax Credit: Hours of work increases below kink point & Hours of work at parallel area the same & Decrease hours of work above second kink point because don't have to work as much due to subsidy & Consumption increases at all levels affected by this be have more money & can consume more & Encourages ppl to join labor force since can receive more benefits from workingWage cuts after you no longer qualify for it, induces ppl to work less at a certain level.

Hoynes (2019) & the Earned Income Tax Credit

• Empirical Analysis of Hoynes (2019) includes evidence about the Earned Income Tax Credit's effects on labor supply behavior . Hypothesis : EITC increases employment, particularly for single mothers.

• EITC Definition

• Gives a subsidy for workers below a certain income threshold As workers continue to earn a higher salary, the subsidy decreases, until it completely disappears. Subsidy benefits don't apply to people w/o jobs

• How the 1993 EITC expansion increased benefits for families with two or more children compared to those with one child & By comparing changes in employment rates between these groups before and after the EITC expansion, it will see the impact of policy effect

  • Treatment: Single women with children & Control: Single women without children
  • The EITC.: Substantial increases to income for low- to moderate-income families largest antipoverty policy in the US: Increase employment among single mothers with children: Positive effect on labor force participation: Married couples also benefit from the program.
  • Low administrative costs are low compared to alternatives. However, as low income workers earn more, the subsidy decreases

EITC Reforms

• Discuss reforms to the EITC suggested in Hoynes (2019): Reforms aimed at equity across family types, In favor of an expansion for childless workers: more significant credit & credit such that it delivers an equitable benefit across different family sizes (thus the credit is equal in equivalence scale terms across groups)., Higher government expenditure, possible work incentive reduction: Reduced poverty, increased labor force participation, Evidence needed.

• The MDRC Paycheck Plus experiment tested a $2,000 credit for childless workers in NYC, finding modest employment gains & Regulate paid tax preparers & - Increased regulatory and administrative expenses.Improved compliance and lower costs for low-income taxpayers,: RS VITA programs (with certified preparers) have lower error rates vs. commercial preparers Studies showing high error rates and predatory fees among commercial tax preparers.

• Reforms aimed at reducing noncompliance - Increased administrative costs for the IRS and compliance burden for self-employed individuals.: Improved accuracy of reported income, reducing overclaims in the EITC program.:Distributing EITC payments periodically over the year rather than as annual lump sums, as this is commonly raised as an impediment to assisting families throughout the year increased administrative complexity and potential overpayments.: Smoothing consumption households and improving financial stability.: -The Chicago EITC Periodic Pilot found high satisfaction (90%) with quarterly payments among participants

Optimal Income Taxation

• Consider optimal income taxation as described in class and Diamond and Saez (2011) optimal tax rate: : a = a measure of the thickness of the top income distribution such that lower “a” implies a thicker tail ( more income at the top)sensitivity of reported income to the ta tax rate g = -a

(g) and the optimal top marginal income tax rate (τ * ). Provide a brief justification for each answer.

• lower tax rate if value on they earn of the highest earners is higher. . &

Labor Demand and the Market

• Firms pay workers according to the value of the marginal product of labor and this value declines as more workers are hired The elasticity of labor demand measures the responsiveness of firms to the amount of employment they demand when there is a change in the market wage -elasticity of substitution capital and labor jobs market Describe three of Marshal

Value of the Marginal Product of Labor

• The value of what is produced as a result of a worker how a labor market with a monopsony differs from a perfectly competitive labor market. Examples of what the model is

Statistical Life

• How explain how you can estimate the value of statistical life (with correlations).
• What value would we need:
  • Gov needs that for cost of value of statistical life.

Compare and Contrast

• Services the Gov provide. What does that do. and for workers and

what does that do and which services would Taxes would induce people to employ less jobs. and might be wise for the policy end.